Inertial navigation systems (INS) are often used to establish the position of a mobile vehicle with respect to an arbitrary starting point. An INS uses a stablized platform attached to the vehicle to detect accelerations experienced by the vehicle. The navigation computer integrates accelerations with respect to time, producing velocity estimates. Integrating these velocity estimates, in turn, with respect to time produces position estimates. Because of the chain of integrations, any bias error in the measurement of the accelerations causes a quadratic error in the position measurement.
The vehicle carrying the stablized platform has its own dynamic response which can be both timevarying and non-linear. This dynamic response obviously affects the accelerations measured by the inertial navigation system. Among the effects caused by this time-varying non-linear dynamic response are the possible introduction of bias errors into the accelerations measured by the inertial navigation system or the masking of bias errors by inertial sensor imperfections.
An example of a time-varying, non-linear system is the inertial navigation system (INS) used to determine the position of an airplane. Of particular interest are applications where data are collected by sensors aboard the aircraft and the interpretation of the data depends upon an accurate knowledge of the true position of the aircraft relative to a fixed earth coordinate system Aircraft-mounted synthetic aperture radar (SAR) systems are examples of such applications.
In a typical SAR application, an aircraft attempts to follow a prescribed trajectory with respect to the ground. At the same time, a sensor in the SAR makes coherent measurements of the radar range to targets generally disposed in directions perpendicular to the direction of travel. These radar measurements are processed onboard the aircraft or recorded on magnetic tape, along with the INS-measured position of the aircraft, for processing later. Any errors in the measurements of position exceeding a certain level lead to distortions in the image formation by the SAR processor. Alternate means can be used to make corrections for inaccuracies in the position measurements resulting from the inevitable failure of the aircraft to exactly follow some intended trajectory. However, because the measurements made by the SAR are subject to the time-varying non-linear dynamic response of the aircraft and sensor errors, these techniques perform inadequately under some conditions, allowing quadratic position errors to defocus the radar image.
It is advantageous, therefore, to have a control system which will add corrections when required and can adapt to the changing dynamics of the system to be controlled and to possibly wide variations in errors, in the absence of any a prior knowledge. It is additionally advantageous to have an adaptive learning control system which will operate with time-varying and non-linear systems and perform according to nonquadratic or quadratic performance criteria.